Backpropagation Imaging in Nonlinear Harmonic Holography in the Presence of Measurement and Medium Noises

TL;DR

This paper investigates the use of second-harmonic generation for detecting small reflectors in noisy, heterogeneous media, demonstrating improved stability and noise resilience of second-harmonic imaging over fundamental frequency imaging.

Contribution

It provides a statistical analysis showing that second-harmonic imaging is more stable against medium noise and its SNR is independent of the particle's properties.

Findings

Second-harmonic images are more stable under medium noise.

Second-harmonic SNR does not depend on particle volume or susceptibility.

Fundamental frequency images are less stable in noisy environments.

Abstract

In this paper, the detection of a small reflector in a randomly heterogenous medium using second-harmonic generation is investigated. The medium is illuminated by a time-harmonic plane wave at frequency omega. It is assumed that the reflector has a non-zero second-order nonlinear susceptibility, and thus emits a wave at frequency two omega in addition to the fundamental frequency linear scattering. It is shown how the fundamental frequency signal and the second-harmonic signal propagate in the medium. A statistical study of the images obtained by migrating the boundary data is performed. It is proved that the second-harmonic image is more stable with respect to medium noise than the one obtained with the fundamental signal. Moreover, the signal-to-noise ratio for the second-harmonic image does not depend neither on the second-order susceptibility tensor nor on the volume of the particle.